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Administrative Unit:Mathematics
College/School: College of Letters & Science
Admitting Plans:M.A., Ph.D.
Degrees Offered:M.A., Ph.D.
Minors and Certificates:Ph.D. Minor
Named Options: Foundations of Advanced Studies (M.A.)
Specializations: Algebra and Number Theory, Analysis and Probability,
Applied and  Computational Mathematics,
Logic, Geometry and Topology

Faculty: Professors: Angenent, Assadi, Bach, Bolotin, Boston, Cai, Chen, Ellenberg, Feldman, Ferris, Gong,  Jin, Kiselev, Lempp, Mari-Beffa, Milewski, Millar, A. Miller, Nagel (chair), Nazarov, Oh, Recht, Ron, Seeger, Seppalainen, Smith, Terwilliger, Viaclovsky, Waleffe, Yang;    Associate Professors: Caldararu, Craciun, Denissov, J. Miller, Mitchell, Paul, Thiffeault, Zlatos;   Assistant Professors: Anderson, Armstrong, Dymarz, Gurevich, Kent, Maxim, Rossmanith, Stechmann, Street, Valko, M. Wood, P. Wood, Yin


The Department of Mathematics offers the master's and the Ph.D. (For actuarial mathematics, contact the School of Business.)

To earn a Ph.D., a student must demonstrate proficiency in basic and advanced graduate mathematics, and must complete a significant piece of original research. To earn a master's degree a student must demonstrate proficiency in basic graduate mathematics as well as a specialty within mathematics or some outside specialty on which mathematics bears. The breadth of the department is such that the Ph.D. specialty and dissertation may be in any area of mathematics, in particular algebra, algebraic geometry, applied mathematics, combinatorics, computational mathematics, complex analysis,  differential equations, differential geometry, harmonic analysis, logic, mathematical biology, number theory, probability,  and  topology. A complete list of faculty and their areas of expertise is available through the department website.


Students interested in mathematics are invited to apply to the Ph.D. program. Applicants who do not intend to study beyond the master's degree are admitted only in exceptional cases. Applicants to the Ph.D. program are automatically considered for financial support. To be admitted for the Ph.D., it is necessary that in the department's opinion the applicant is likely to complete the program. This, of course, is a highly subjective judgment. The department does welcome applications from other outstanding students whose background and credentials  do not match the description below.

Admission requirements are:

  1. An overall GPA of at least 3.0 (on a 4.0 scale) and substantially higher in mathematics courses.
  2. 18 or more credits of mathematics beyond calculus. The 18 credits should include at least one semester of both rigorous analysis (sometimes called advanced calculus) and abstract algebra, and preferably two semesters. Other advanced undergraduate and graduate courses in mathematics further strengthen the application.
  3. Official transcripts or academic records from each institution attended. International academic records must be in the original language accompanied by an official English translation. Documents must be issued by the school with the official seal/stamp and an official signature. Send two transcript(s) to the mathematics department only (address below).
  4. Create a list of mathematics courses taken. This is indicated on the Supplemental Application Form. It is important to include the most advanced mathematics courses the applicant has completed, is currently enrolled in, or intends to take. For each course include the name of the school where it was taken, the course number, the title and description, textbooks used, and the grade received (for completed courses). A transcript does not suffice for this list.
  5. A statement of reasons for graduate study.
  6. GRE (Graduate Record Exam) scores, including the advanced subject test in mathematics. In exceptional cases, advanced GRE scores from other sciences can be substituted for the advanced GRE in mathematics. All scores should be received online from ETS by mid-January. For students who have taken the exam by December 15, this should not present a problem. For those who take the exam in late December or thereafter , scores will not reach the department in time. Applicants should have ETS electronically submit their scores, using the UW–Madison institution code of 1846. (There is no department code.)
  7. Three letters of recommendation that address the question of mathematical promise. These letters should be from mathematics faculty, or other faculty familiar with the demands of graduate work in mathematics. Please note that the department does not require forms for letters of recommendation. Recommenders should submit letters electronically as indicated in the instructions of the online application.
  8. Applicants whose native language is not English, or whose undergraduate instruction was not in English, must provide official scores from the TOEFL (Test of English as a Foreign Language) or the IELTS (International English Language Testing System). Competitive scores for the TOEFL are 630 (paper), 267 (computer), 109 (iBT) or above. A competitive score for IELTS is 7. After acceptance, international students with TA appointments must attend the summer (early July to mid August) TA training and orientation program and successfully pass the SPEAK test of spoken English (given on campus). Attendees are given some financial support during the orientation.
  9. The nonrefundable application fee can be paid electronically with the online application or sent to the Graduate School, 217 Bascom Hall, 500 Lincoln Drive, Madison, WI 53706. The department is not able to waive this fee.
  10. Please see the mathematics department website for more detailed information about the program and the application process.

An applicant who does not meet all departmental expectations may be admitted on probation, provided there is evidence of mathematical promise. Such promise is evidenced by high GRE scores or by comments from mathematics faculty.

For more information: Graduate Program Administrator, Department of Mathematics, Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706; tel: 608-263-8884; grad_program@math.wisc.edu; http://www.math.wisc.edu/graduate/admissions